#1126 ⟨a, b | ababba=bab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. ab(ac)2 ⇒ cb [4]
2. a4bac3 ⇒ bac2a [30]
3. ca3bac3 ⇒ bc3a [31]
4. bab ⇒ abac [3]
5. bcb ⇒ cbac [7]
6. a2bac2b ⇒ bac2 [18]
7. cabac2b ⇒ bc3 [19]
8. b2a ⇒ c [2]
9. abacba ⇒ bac [5]
10. (cba)2 ⇒ bc2 [9]
11. bac2ba ⇒ a2bac3 [14]
12. bc3ba ⇒ cabac3 [17]
13. ba2bac ⇒ abacab [6]
14. bcabac ⇒ cbacab [10]
15. (bac)2 ⇒ abac2b [8]
16. bc2bac ⇒ cbac2b [11]
17. (abac)2 ⇒ bacb [12]
18. cbacabac ⇒ bc2b [16]
19. bac2abac ⇒ a2bac3b [22]
20. bc3abac ⇒ cabac3b [23]
21. a2bac3bac ⇒ bac3b [20]
22. cabac3bac ⇒ bc4b [21]
23. b2c2 ⇒ cb(ac)2ba [15]
24. bacbc2 ⇒ a2bac4ba [28]
25. (bc2)2 ⇒ cabac4ba [34]
26. abacabc2 ⇒ c3ba [13]
27. ba3bac3 ⇒ c2baca [24]
28. bca2bac3 ⇒ cbacac2ba [25]
29. bacabac3 ⇒ abac4ba [32]
30. bc2abac3 ⇒ cbac4ba [33]
31. baca2bac3 ⇒ abac3baca [26]
32. bc2a2bac3 ⇒ cbac3baca [27]
33. bac2a2bac3 ⇒ a2bac5ba [29]
34. bc3a2bac3 ⇒ cabac5ba [35]
35. a(abac3)2 ⇒ bac5ba [36]
36. c(abac3)2 ⇒ bc6ba [37]
37. (a2bac3)2 ⇒ bac4baca [38]
38. cabac3a2bac3 ⇒ bc5baca [39]
# ab:ababba=bab reversed:ac/b bba=c morph:3/1
abacac=cb
aaaabaccc=bacca
caaabaccc=bccca
bab=abac
bcb=cbac
aabaccb=bacc
cabaccb=bccc
bba=c
abacba=bac
cbacba=bcc
baccba=aabaccc
bcccba=cabaccc
baabac=abacab
bcabac=cbacab
bacbac=abaccb
bccbac=cbaccb
abacabac=bacb
cbacabac=bccb
baccabac=aabacccb
bcccabac=cabacccb
aabacccbac=bacccb
cabacccbac=bccccb
bbcc=cbacacba
bacbcc=aabaccccba
bccbcc=cabaccccba
abacabcc=cccba
baaabaccc=ccbaca
bcaabaccc=cbacaccba
bacabaccc=abaccccba
bccabaccc=cbaccccba
bacaabaccc=abacccbaca
bccaabaccc=cbacccbaca
baccaabaccc=aabacccccba
bcccaabaccc=cabacccccba
aabacccabaccc=bacccccba
cabacccabaccc=bccccccba
aabacccaabaccc=baccccbaca
cabacccaabaccc=bcccccbaca

Other submonoids of same group

11 unique, 55 total

Σ#PresentationDescriptionRelated
6104⟨a, b | aaba=bb⟩Infinite cancellative non-commutative monoid
7145⟨a, b | aababba=1⟩Infinite non-Abelian group22 iso, 22 anti-iso
7193⟨a, b | ababba=b⟩Infinite cancellative non-commutative monoid
7252⟨a, b | aaba=bab⟩Infinite cancellative non-commutative monoid
9842⟨a, b | abaababa=b⟩Infinite cancellative non-commutative monoid
91273⟨a, b | abbba=babb⟩Infinite cancellative non-commutative monoid
102633⟨a, b | abbbba=babb⟩Infinite cancellative non-commutative monoid
113716⟨a, b | abaaabaaba=b⟩Infinite cancellative non-commutative monoid
114876⟨a, b | abbabbba=bab⟩Infinite cancellative non-commutative monoid
115415⟨a, b | abbbbba=babb⟩Infinite cancellative non-commutative monoid
115898⟨a, b | ababba=babab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationDescriptionRelated
687⟨a, b | aabba=b⟩Infinite cancellative non-commutative monoid
7179⟨a, b | aababa=b⟩Infinite cancellative non-commutative monoid
8374⟨a, b | aabaaba=b⟩Infinite cancellative non-commutative monoid
8586⟨a, b | baab=aaba⟩Infinite cancellative non-commutative monoid
9792⟨a, b | aabaaaba=b⟩Infinite cancellative non-commutative monoid
101666⟨a, b | aabaaaaba=b⟩Infinite cancellative non-commutative monoid
113536⟨a, b | aabaaaaaba=b⟩Infinite cancellative non-commutative monoid